Translocation of a heterogeneous polymer

We present results on the sequence dependence of translocation kinetics for a partially charged heteropolymer moving through a very thin pore using theoretical tools and Langevin dynamics simulational techniques. The chain is composed of two types of monomers of differing frictional interaction with the pore and charge. We present exact analytical expressions for passage probability, mean first passage time, and mean successful passage times for both reflecting/absorbing and absorbing/absorbing boundary conditions, showing rich and unexpected dependence of translocation behavior on charge fraction, distribution along the chain, and electric field configuration. We find excellent qualitative and good quantitative agreement between theoretical and simulation results. Surprisingly, there emerges a threshold charge fraction of a diblock copolymer beyond which the success rate of translocation is independent of charge fraction. Also, the mean successful translocation time of a diblock copolymer displays non-monotonic behavior with increasing length of the charged block; there is an optimum length of the charged block where the mean translocation rate is the slowest; and there can be a substantial range of higher charge fractions which make the translocation slower than even a minimally charged chain. Additionally, we find for a fixed total charge on the chain, finer distribution along the backbone significantly decreases mean translocation time.     

Polymer translocation through a nanopore under an applied external field

We investigate the dynamics of polymer translocation through a nanopore under an externally applied field using the two-dimensional fluctuating bond model with single-segment Monte Carlo moves. We concentrate on the influence of the field strength E, length of the chain N, and length of the pore L on forced translocation. As our main result, we find a crossover scaling for the translocation time tau with the chain length from tau approximately N2nu for relatively short polymers to tau approximately N1+nu for longer chains, where nu is the Flory exponent. We demonstrate that this crossover is due to the change in the dependence of the translocation velocity v on the chain length. For relatively short chains v approximately N-nu, which crosses over to v approximately N(-1) for long polymers. The reason for this is that with increasing N there is a high density of segments near the exit of the pore, which slows down the translocation process due to slow relaxation of the chain. For the case of a long nanopore for which R parallel, the radius of gyration Rg along the pore, is smaller than the pore length, we find no clear scaling of the translocation time with the chain length. For large N, however, the asymptotic scaling tau approximately N1+nu is recovered. In this regime, tau is almost independent of L. We have previously found that for a polymer, which is initially placed in the middle of the pore, there is a minimum in the escape time for R parallel approximately L. We show here that this minimum persists for weak fields E such that EL is less than some critical value, but vanishes for large values of EL.     

Langevin dynamics simulations of polymer translocation through nanopores

We investigate the dynamics of polymer translocation through a nanopore using two-dimensional Langevin dynamics simulations. In the absence of an external driving force, we consider a polymer which is initially placed in the middle of the pore and study the escape time tau(e) required for the polymer to completely exit the pore on either side. The distribution of the escape times is wide and has a long tail. We find that tau(e) scales with the chain length N as tau(e) approximately N(1+2nu), where nu is the Flory exponent. For driven translocation, we concentrate on the influence of the friction coefficient xi, the driving force E, and the length of the chain N on the translocation time tau, which is defined as the time duration between the first monomer entering the pore and the last monomer leaving the pore. For strong driving forces, the distribution of translocation times is symmetric and narrow without a long tail and tau approximately E(-1). The influence of xi depends on the ratio between the driving and frictional forces. For intermediate xi, we find a crossover scaling for tau with N from tau approximately N(2nu) for relatively short chains to tau approximately N(1+nu) for longer chains. However, for higher xi, only tau approximately N(1+nu) is observed even for short chains, and there is no crossover behavior. This result can be explained by the fact that increasing xi increases the Rouse relaxation time of the chain, in which case even relatively short chains have no time to relax during translocation. Our results are in good agreement with previous simulations based on the fluctuating bond lattice model of polymers at intermediate friction values, but reveal additional features of dependency on friction.     

Polymer translocation through a nanopore. II. Excluded volume effect

Following our previous study of a Gaussian chain translocation, we have investigated the transport of a self-avoiding chain from one sphere to another sphere through a narrow pore, using the self-consistent field theory formalism. The free energy landscape for polymer translocation is significantly modified by excluded volume interactions among monomers. The free energy barrier for the placement of one of the chain ends at the pore depends on the chain length N nonmonotonically, in contrast to the N-independence for Gaussian chains. This results in a nonmonotonic dependence of the average arrival time [tau0] on N for self-avoiding chains. When the polymer chain is partitioned between the donor and recipient spheres, a local free energy minimum develops, depending on the strength w of the excluded volume interaction and the relative sizes of the donor and recipient spheres. If the sizes of spheres are comparable, the average translocation time tau (the average time taken by the polymer, after the arrival at the pore, to convert from the donor to the recipient) increases with an increase in w for a fixed N value. On the other hand, for the highly asymmetric sizes of the donor and recipient spheres, tau decreases with an increase in w. As in the case of Gaussian chains, tau depends nonmonotonically on the pore length.     

Polymer translocation through a nanopore induced by adsorption: Monte Carlo simulation of a coarse-grained model

Dynamic Monte Carlo simulation of a bead-spring model of flexible macromolecules threading through a very narrow pore in a very thin rigid membrane are presented, assuming at the cis side of the membrane a purely repulsive monomer-wall interaction, while the trans side is attractive. Two choices of monomer-wall attraction epsilon are considered, one choice is slightly below and the other slightly above the "mushroom to pancake" adsorption threshold epsilon(c) for an infinitely long chain. Studying chain lengths N=32, 64, 128, and 256 and varying the number of monomers N(trans) (time t=0) that have already passed the pore when the simulation started, over a wide range, we find for epsilonepsilon(c) a finite number N(trans)(t=0) suffices that the translocation probability is close to unity. In the case epsilonepsilon(c), we find that the translocation time scales as tau proportional, variant N(1.65+/-0.08). We suggest a tentative scaling explanation for this result. Also the distribution of translocation times is obtained and discussed.     

Translocation of a protein-like chain through an interacting channel

The effect of channel-protein interaction on the translocation of a protein-like chain through a finite channel under certain electric field was studied by using dynamical Monte Carlo simulations.The interior behavior of chain conformation under different interactions was investigated,such as the number of monomers outside of channel n_out,monomers inside of channel n_m,mean-square radius of gyration〈S²〉and the average energy〈U〉.It shows that with strong attractive interaction,the translocation is more difficult than moderate interaction.At the same time,the dependence of translocation time with different interactions shows that moderate repulsive interaction(ε_cp= 0.5) accelerates the translocation.Although the waiting time for successful translocation ofε_cp = 1.0 is the longest,the average translocation time is not very large.It is far smaller than that ofε_cp=-1.0.The probability distributions of translocation time p（t’） and the probability distributions of three duration times p（t₁’）,p（t₂’） and p（t₃’） were all discussed.Log-normal distributions are found.All these findings will strengthen the understanding of protein translocation.     

Polymer translocation: the effect of backflow

We investigate the effect of backflow on the translocation dynamics of short, flexible polymer chains threading through a small hole in a wall. We find that hydrodynamic interactions between polymer beads play an important role in determining the translocation time distribution: as a monomer moves through the hole it sets up a flow field which transfers momentum to neighboring monomers, thus helping them to move in the same direction. Translocation times are calculated by using the velocity-Verlet algorithm to solve the equations of motion of a polymer which moves in a fluid described by the stochastic rotation algorithm, a particle-based Navier-Stokes solver.     

A Monte Carlo algorithm to study polymer translocation through nanopores. II. Scaling laws

In the first paper of this series, we developed a new one-dimensional Monte Carlo approach for the study of flexible chains that are translocating through a small channel. We also presented a numerical scheme that can be used to obtain exact values for both the escape times and the escape probabilities given an initial pore-polymer configuration. We now present and discuss the fundamental scaling behaviors predicted by this Monte Carlo method. Our most important result is the fact that, in the presence of an external bias E, we observe a change in the scaling law for the translocation time tau as function of the polymer length N: In the general expression tau approximately N(beta)E, the exponent changes from beta=1 for moderately long chains to beta=1+nu or beta=2nu for very large values of N (for Rouse and Zimm dynamics, respectively). We also observe an increase in the effective diffusion coefficient due to the presence of entropic pulling on unbiased polymer chains.     

Heteropolymer translocation through nanopores

The authors investigate the translocation dynamics of heteropolymers driven through a nanopore using a constant temperature Langevin thermostat. Specifically, they consider heteropolymers consisting of two types of monomers labeled A and B, which are distinguished by the magnitude of the driving force that they experience inside the pore. From a series of studies on polymers with sequences AmBn the authors identify both universal as well as specific sequence properties of the translocating chains. They find that the scaling of the average translocation time as a function of the chain length N remains unaffected by the heterogeneity, while the residence time of each bead is a strong function of the sequence for short repeat units. They further discover that for a symmetric heteropolymer AnBn of fixed length, the pattern exhibited by the residence times of the individual monomers has striking similarity with a double slit interference pattern where the total number of repeat units N/2n controls the number of interference fringes. These results are relevant for designing nanopore based sequencing techniques.     

Static and dynamic properties of tethered chains at adsorbing surfaces: a Monte Carlo study

We present extensive Monte Carlo simulations of tethered chains of length N on adsorbing surfaces, considering the dilute case in good solvents, and analyze our results using scaling arguments. We focus on the mean number M of chain contacts with the adsorbing wall, on the chain's extension (the radius of gyration) perpendicular and parallel to the adsorbing surface, on the probability distribution of the free end and on the density profile for all monomers. At the critical adsorption strength epsilon(c) one has M(c) approximately N(phi), and we find (using the above results) as best candidate phi to equal 0.59. However, slight changes in the estimation of epsilon(c) lead to large deviations in the resulting phi; this might be a possible reason for the difference in the phi values reported in the literature. We also investigate the dynamical scaling behavior at epsilon(c), by focusing on the end-to-end correlation function and on the correlation function of monomers adsorbed at the wall. We find that at epsilon(c) the dynamic scaling exponent a (which describes the relaxation time of the chain as a function of N) is the same as that of free chains. Furthermore, we find that for tethered chains the modes perpendicular to the surface relax quicker than those parallel to it, which may be seen as a splitting in the relaxation spectrum.     

Mathematical model for DNA separation by capillary electrophoresis in entangled polymer solutions

A mathematical model of DNA separation by capillary electrophoresis in entangled polymer solution is presented. The mechanism is modeled as a DNA molecule moving through transient pores formed in polymer solutions and colliding with blobs of polymer molecules encountered during migration. By taking account of the average retardation time (t(c)) of DNA-blob collision and calculating the total collision number (N(c)), a quantitative mathematical equation was reported, leading to predictions for the DNA mobility as a function of the experimental conditions like the size of DNA, the polymer concentration and the electric field strength. For DNA fragments in frequent size range, the initial experimental data agree well with the model. The DNA shape function (f(E)) was suggested and then discussed by the experimental data. The relationship between f(E) and electric field strength E was empirically estimated. Then, the average retardation time t(c) was obtained as about (2 approximately 3)x10(-6)s in linear polyacrylamide (LPA) and hydroxyethylcellulose (HEC) solution.     

Simulation study of the coil-globule transition of a polymer in solvent

Molecular dynamics simulations are used to study the coil-globule transition for a system composed of a bead-spring polymer immersed in an explicitly modeled solvent. Two different versions of the model are used, which are differentiated by the nature of monomer-solvent, solvent-solvent, and nonbonded monomer-monomer interactions. For each case, a model parameter lambda determines the degree of hydrophobicity of the monomers by controlling the degree of energy mismatch between the monomers and solvent particles. We consider a lambda-driven coil-globule transition at constant temperature. The simulations are used to calculate average static structure factors, which are then used to determine the scaling exponents of the system in order to determine the theta-point values lambdatheta separating the coil from the globule states. For each model we construct coil-globule phase diagrams in terms of lambda and the particle density rho. The results are analyzed in terms of a simple Flory-type theory of the collapse transition. The ratio of lambdatheta for the two models converges in the high density limit exactly to the value predicted by the theory in the random mixing approximation. Generally, the predicted values of lambdatheta are in reasonable agreement with the measured values at high rho, though the accuracy improves if the average chain size is calculated using the full probability distribution associated with the polymer-solvent free energy, rather than merely using the value obtained from the minimum of the free energy.     

Diffusion constant in gel electrophoresis at high fields

We present new measurements of the diffusion constant D in standard (slab-gel) electrophoresis of DNA at fields up to 10 V/cm. Molecules investigated are bacteriophages: T4 of length 173 kbp and lambda of length 48.5 kbp cut by restriction enzyme HindIII. We show, that D increases with the molecule length for electric field E above 5 V/cm. The results are interpreted within the geometration model.     

Adsorption-driven translocation of polymer chain into nanopores

The polymer translocation into nanopores is generally facilitated by external driving forces, such as electric or hydrodynamic fields, to compensate for entropic restrictions imposed by the confinement. We investigate the dynamics of translocation driven by polymer adsorption to the confining walls that is relevant to chromatographic separation of macromolecules. By using the self-consistent field theory, we study the passage of a chain trough a small opening from cis to trans compartments of spherical shape with adsorption potential applied in the trans compartment. The chain transfer is modeled as the Fokker-Plank diffusion along the free energy landscape of the translocation pass represented as a sum of the free energies of cis and trans parts of the chain tethered to the pore opening. We investigate how the chain length, the size of trans compartment, the magnitude of adsorption potential, and the extent of excluded volume interactions affect the translocation time and its distribution. Interplay of these factors brings about a variety of different translocation regimes. We show that excluded volume interactions within a certain range of adsorption potentials can cause a local minimum on the free energy landscape, which is absent for ideal chains. The adsorption potential always leads to the decrease of the free energy barrier, increasing the probability of successful translocation. However, the translocation time depends non-monotonically of the magnitude of adsorption potential. Our calculations predict the existence of the critical magnitude of adsorption potential, which separates favorable and unfavorable regimes of translocation.     

Electrohydrodynamics of spherical polyampholyte‐grafted nanoparticles: Multiscale simulations by coupling of molecular dynamics and lattice‐boltzmann method

We perform multiscale simulations based on the coupling of molecular dynamics and lattice‐Boltzmann (LB) method to study the electrohydrodynamics of a polyampholyte‐grafted spherical nanoparticle. The long‐range hydrodynamic interactions are modeled by coupling the movement of particles to a LB fluid. Our results indicate that the net‐neutral soft particle moves with a nonzero mobility under applied electric fields. We systematically explore the effects of different parameters, including the chain length, grafting density, electric field, and charge sequence, on the structures of the polymer layer and the electrophoretic mobility of the soft particle. It shows that the mobility of nanoparticles has remarkable dependence on these parameters. We find that the deformation of the polyampholyte chains and the ion distribution play dominant roles in modulating the electrokinetic behavior of the polyampholyte‐grafted particle. The enhancement or reduction in the accumulation of counterions around monomers can be attributed to the polymer layer structure and the conformational transition of the chains in the electric field. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1435–1447     

Adsorption of semiflexible block copolymers on homogeneous surfaces

We present the results of extensive numerical off-lattice Monte Carlo simulations of semiflexible block-copolymer chains adsorbed onto flat homogeneous surfaces. We have compared the behavior of several chain structures, such as homopolymers, diblocks, (A(alpha)B(alpha)) block copolymers, and random heteropolymers. In all the cases studied, we have found the adsorption process to be favored with an increase of the chain rigidity. Particularly, the adsorption of diblock structures becomes a two-step process characterized by two different adsorbing temperatures that depend on the chain stiffness kappa, the chain length N, and the adsorbing energies epsilon(A) and epsilon(B). This twofold adsorbing process changes to a single one for copolymers of reduced block size alpha. Each block of the stiff copolymer chain is found to satisfy the classical scaling laws for flexible chains, however, we found the scaling exponent phi to depend on the chain stiffness. The measurement of the radius of gyration exhibits a typical behavior of a polymer chain composed of Nl(p) blobs whose persistence length follows l(p) approximately (kappa/k(B)T)(0.5) for large stiff chains.     

Scaling law of poly(ethylene oxide) chain permeation through a nanoporous wall

This paper presents a study of the permeation of poly(ethylene oxide) (PEO) chains through the nanoporous wall of hollow polymeric capsules prepared by self-assembly of polyelectrolytes. We employ the method of pulsed field gradient (PFG) NMR diffusion to distinguish chains in different sites, i.e., in the capsule interior and free chains in the dispersion, by their respective diffusion coefficient. From a variation of the observation time, the time scale of the molecular exchange between both sites and thus the permeation rate constant is extracted from a two-site exchange model. Permeation rate constants show two different regimes with a different dependence on chain length. This suggests a transition between two different mechanisms of permeation as the molecular weight is increased. In either regime, the permeation time can be described by a scaling law tau approximately N (b) , with b = (4)/ 3 for short chains and b = (1)/ 3 for long chains. We discuss these exponents, which clearly differ from the theoretical predictions for chain translocation.     

Theory of sequence effects on DNA translocation through proteins and nanopores

A general formula for the sequence effects on the average translocation time of a polymer passing through a narrow hole under a chemical potential gradient is provided. The utility of the general expression is illustrated by considering the diblock sequence of a polymer with two kinds of monomers. The experimental conditions required for sufficient discrimination of various sequences are addressed.     

Structural and spectroscopic studies of peptoid oligomers with alpha-chiral aliphatic side chains

Substantial progress has been made in the synthesis and characterization of various oligomeric molecules capable of autonomous folding to well-defined, repetitive secondary structures. It is now possible to investigate sequence-structure relationships and the driving forces for folding in these systems. Here, we present detailed analysis by X-ray crystallography, NMR, and circular dichroism (CD) of the helical structures formed by N-substituted glycine (or "peptoid") oligomers with alpha-chiral, aliphatic side chains. The X-ray crystal structure of a N-(1-cyclohexylethyl)glycine pentamer, the first reported for any peptoid, shows a helix with cis-amide bonds, approximately 3 residues per turn, and a pitch of approximately 6.7 A. The backbone dihedral angles of this pentamer are similar to those of a polyproline type I peptide helix, in agreement with prior modeling predictions. This crystal structure likely represents the major solution conformers, since the CD spectra of analogous peptoid hexamers, dodecamers, and pentadecamers, composed entirely of either (S)-N-(1-cyclohexylethyl)glycine or (S)-N-(sec-butyl)glycine monomers, also have features similar to those of the polyproline type I helix. Furthermore, this crystal structure is similar to a solution NMR structure previously described for a peptoid pentamer comprised of chiral, aromatic side chains, which suggests that peptoids containing either aromatic or aliphatic alpha-chiral side chains adopt fundamentally similar helical structures in solution, despite distinct CD spectra. The elucidation of detailed structural information for peptoid helices with alpha-chiral aliphatic side chains will facilitate the mimicry of biomolecules, such as transmembrane protein domains, in a distinctly stable form.     

Electric field amplification of plasmon-molecule hybrids revealed by first-principles time dependent density functional theory calculations

Using first-principles quantum mechanical calculations, we investigate the electric field amplification in hybrid nanostructures composed of few-atom Ni linear chains attached to an organic molecule. We found that the pristine Ni linear chains exhibit localized plasmons and produce nanoscale hotspot regions, acting as a plasmon-like nanoantenna. We demonstrate that localized plasmons provide massive electric field amplification in the vicinity of the molecule. Besides, we also investigated the active modulation of the optical absorption spectra due to the inclusion of a positive and/or negative electric field in the Hamiltonian. We believe that the results presented in this work are important for the emerging field of cavity induced photo-catalysis and will aid in the realization of new quantum nano-optic devices.